1、在隨機時間序列分析中，為簡便起見，我們假定時間序列主要由趨勢項（T）、季節項（S）和隨機項（R）構成。#讀入數據，畫曲線圖> sales <- read.csv(file = "sales.csv",header = TRUE)> head(sales)> plot(sales$t,sales$Y,type = "l")o10203040sales St觀察這幅圖形，可以看出有明顯的長期趨勢和季節變動。利用分解法，假設這48個數據可表示為：¥ Tt Ct S It，Yt代表實 際銷售額度。長期趨勢的分解用時間回歸法，在同

2、一圖中畫出趨勢項目、季節項和隨機項的數據圖，女口下：decompose。 函數主要用來做季節指數分解，figure 項即指季節指數。同時 也返回原始數據，以及MA算法的結果；trend 趨勢項使用光滑移動平均法求得， 它包含了長期趨勢T和周期變動因素C,之前用回歸法求得長期趨勢T,利用此 函數的返回值Trend即可求得周期變動因素C； Random即為不規則變動。 此函數的基本結構：Additive:xtMultiplicative:=Trend + Seas onal + Ran dom xt = Trend * Seas onal * Ran dom> salesl <- ts

3、(sales,2,start = 1,freque ncy = 4)#季節變動趨勢分解> m <- decompose(sales1,type = "multiplicative")> plot(m)> m $xQtr1 Qtr2 Qtr3 Qtr42003 3017.60 3043.54 2094.35 2809.842004 3274.80 3163.28 2114.31 3024.572005 3327.48 3493.48 2439.93 3490.792006 3685.08 3661.23 2378.43 3459.552007 3849

4、.63 3701.18 2642.38 3585.522008 4078.66 3907.06 2828.46 4089.502009 4339.61 4148.60 2916.45 4084.642010 4242.42 3997.58 2881.01 4036.232011 4360.33 4360.53 3172.18 4223.762012 4690.48 4694.48 3342.35 4577.632013 4965.46 5026.05 3470.14 4525.942014 5258.71 5189.58 3596.76 3881.60$seasonalQtr1 Qtr2 Qt

5、r3 Qtr42003 1.1213967 1.0938549 0.7535947 1.03115372004 1.1213967 1.0938549 0.7535947 1.03115372005 1.1213967 1.0938549 0.7535947 1.03115372006 1.1213967 1.0938549 0.7535947 1.03115372007 1.1213967 1.0938549 0.7535947 1.03115372008 1.1213967 1.0938549 0.7535947 1.03115372009 1.1213967 1.0938549 0.75

6、35947 1.03115372010 1.1213967 1.0938549 0.7535947 1.03115372011 1.1213967 1.0938549 0.7535947 1.03115372012 1.1213967 1.0938549 0.7535947 1.03115372013 1.1213967 1.0938549 0.7535947 1.03115372014 1.1213967 1.0938549 0.7535947 1.0311537$trend (居中平均TC)Qtr1 Qtr2 Qtr3 Qtr42003 NA NA 2773.483 2820.600200

7、4 2838.062 2867.399 2900.825 2948.6852005 3030.662 3129.642 3232.620 3298.2892006 3311.570 3299.977 3316.641 3342.2042007 3380.191 3428.931 3473.306 3527.6702008 3576.665 3662.923 3758.539 3821.3502009 3862.541 3872.932 3860.176 3829.1502010 3805.843 3795.361 3804.049 3864.1562011 3945.921 4005.759

8、4070.469 4153.4812012 4216.496 4282.001 4360.608 4436.4262013 4493.846 4503.359 4533.554 4590.6512014 4626.920 4562.205 NA NA$ra ndom（不規則變動）Qtr1 Qtr2 Qtr3 Qtr42003 NA NA 1.0020422 0.96608802004 1.0289720 1.0085324 0.9671844 0.99474522005 0.9790810 1.0204784 1.0015782 1.02638812006 0.9923245 1.014276

9、4 0.9515991 1.00383722007 1.0155901 0.9867832 1.0095187 0.98569102008 1.0169040 0.9751303 0.9986037 1.03783902009 1.0018860 0.9792688 1.0025581 1.03449402010 0.9940394 0.9629070 1.0049880 1.01297282011 0.9853980 0.9951643 1.0341310 0.98619672012 0.9919877 1.0022614 1.0171081 1.00065412013 0.9853307

10、1.0203063 1.0157116 0.95611712014 1.0135098 1.0399147 NA NA$figure（季節變動指數）1 1.1213967 1.0938549 0.7535947 1.0311537$type1 "multiplicative"attr（，“class"）1 "decomposed.ts"呂口Inosm- QDQH 8S-呂呂 CMcpCMn 呂960PQJAJ2 如 qoPUW4 -e匸 OSH如 EQPUffl觀察趨勢圖，可以發現明顯的呈現直線上升的趨勢，所有采用線性回歸擬合。> Im.

11、fit <- lm(Y t,data = sales)> summary(lm.fit)Call:lm(formula = Y t, data = sales)Residuals:Min 1Q Media n3Q Max-1062.7 -724.4 241.7 384.8 769.7Coefficie nts:Estimate Std. Error t value Pr(>|t|)(In tercept) 2736.101168.642 16.224 < 2e-16 *t38.9545.992 6.501 5.11e-08 *Signif. codes: 0'

12、* ' 0.001' * ' 0.01' *' 0.05'. ' 0.1' '1Residual sta ndard error: 575.1 on 46 degrees of freedomMultiple R-squared: 0.4789,Adjusted R-squared: 0.4675F-statistic: 42.27 on 1 and 46 DF, p-value: 5.115e-08由此，長期趨勢方程為：T=2736.10+38.95t，利用此方程即可求得每個季度的趨勢值。#長期趨勢預測> Im.p

13、redict <- predict(lm.fit,n ewdata = data.frame(t = seq(1:48)> Im.predict> pre15 <- predict(lm.fit, newdata = data.frame(t = 49)> pre1514644.865周期變動因素c：采取百分比率，其值大于100的表明該季度經濟活動水平高于所有季度的平 均值，而小于100的循環指數所表明的情況則剛好相反。#周期變動C> c <- m$tre nd/lm.predict> write.csv(rou nd(c,4),file = &

14、quot;sales2.csv")decompose()函數主要用來做季節指數分解，figure項即指季節指數。同時也返回原始數據，以及MA算法的結果；trend趨勢項使用光滑移動平均法求得，它包含了長期趨勢T和周期變動因素C,之前用回歸法求得長期趨勢T,利用此 函數的返回值Trend即可求得周期變動因素C； Random即為不規則變動。 此函數的基本結構：Additive:xt = Trend + Seas onal + Ran domMultiplicative:xt = Trend * Seas onal * Ran dom> salesl <- ts(sales,

15、2,start = 1,freque ncy = 4)#季節變動趨勢分解> m <- decompose(sales1,type = "multiplicative")> plot(m)> m $xQtr1 Qtr2 Qtr3 Qtr42003 3017.60 3043.54 2094.35 2809.842004 3274.80 3163.28 2114.31 3024.572005 3327.48 3493.48 2439.93 3490.792006 3685.08 3661.23 2378.43 3459.552007 3849.63 370

16、1.18 2642.38 3585.522008 4078.66 3907.06 2828.46 4089.502009 4339.61 4148.60 2916.45 4084.642010 4242.42 3997.58 2881.01 4036.232011 4360.33 4360.53 3172.18 4223.762012 4690.48 4694.48 3342.35 4577.632013 4965.46 5026.05 3470.14 4525.94 2014 5258.71 5189.58 3596.76 3881.60$seasonalQtr1 Qtr2 Qtr3 Qtr

17、42003 1.1213967 1.0938549 0.7535947 1.0311537 2004 1.1213967 1.0938549 0.7535947 1.0311537 2005 1.1213967 1.0938549 0.7535947 1.0311537 2006 1.1213967 1.0938549 0.7535947 1.0311537 2007 1.1213967 1.0938549 0.7535947 1.0311537 2008 1.1213967 1.0938549 0.7535947 1.0311537 2009 1.1213967 1.0938549 0.75

18、35947 1.0311537 2010 1.1213967 1.0938549 0.7535947 1.0311537 2011 1.1213967 1.0938549 0.7535947 1.0311537 2012 1.1213967 1.0938549 0.7535947 1.0311537 2013 1.1213967 1.0938549 0.7535947 1.0311537 2014 1.1213967 1.0938549 0.7535947 1.0311537$trend （居中平均 TC ）Qtr1 Qtr2 Qtr3 Qtr42003 NA NA 2773.483 2820

19、.6002004 2838.062 2867.399 2900.825 2948.685 2005 3030.662 3129.642 3232.620 3298.289 2006 3311.570 3299.977 3316.641 3342.204 2007 3380.191 3428.931 3473.306 3527.670 2008 3576.665 3662.923 3758.539 3821.350 2009 3862.541 3872.932 3860.176 3829.150 2010 3805.843 3795.361 3804.049 3864.156 2011 3945.921 4005.759 4070.469 4153.481 2012 4216.496 4282.001 4360.608 4436.426 2013 4493.846 4503.359 4533.554 4590.651 2014 4626.920 4562.205 NA NA $random （不規則變動）Qtr1 Qtr2 Qtr3 Q